Ray's Algebra, Part First: On the Analytic and Inductive Methods of Instruction, with Numerous Practical Exercises, Designed for Common Schools and Academies |
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Page 6
... PROPORTION . Arithmetical Progression • 220-225 222-227 Geometrical Progression · • 226-230 228-232 Ratio Proportion · . 231-239 232-234 . 240-255 231-210 RAY'S ALGEBRA , PART FIRST . INTELLECTUAL EXERCISES . LESSON vi CONTENTS .
... PROPORTION . Arithmetical Progression • 220-225 222-227 Geometrical Progression · • 226-230 228-232 Ratio Proportion · . 231-239 232-234 . 240-255 231-210 RAY'S ALGEBRA , PART FIRST . INTELLECTUAL EXERCISES . LESSON vi CONTENTS .
Page 120
... Proportion , in order to solve it , the pupil must be familiar with these subjects . In the following examples , the learner is sup- posed to be acquainted with Ratio and Proportion , as far as they are taught in Arithmetic . ( See ...
... Proportion , in order to solve it , the pupil must be familiar with these subjects . In the following examples , the learner is sup- posed to be acquainted with Ratio and Proportion , as far as they are taught in Arithmetic . ( See ...
Page 126
... proportion to each other as 2 to 3 . Let 2x one part ; then 3x = the other , since 2x is to 3x as 2 is to 3 . 2x + 3x = 55 5x – 55 x = 11 2x = 22 3x = 33 } Ans . Or thus : Let x = one part ; then 55 - x = the other . By the question , x ...
... proportion to each other as 2 to 3 . Let 2x one part ; then 3x = the other , since 2x is to 3x as 2 is to 3 . 2x + 3x = 55 5x – 55 x = 11 2x = 22 3x = 33 } Ans . Or thus : Let x = one part ; then 55 - x = the other . By the question , x ...
Page 127
... proportion to each other as the numbers 3 , 5 , 7 , and 8. Ans . 12 , 20 , 28 , and 32 . 28. Divide the number 60 into 3 such parts , that of the first , of the second , and of the third , shall all be equal to each other . Ans . 12 ...
... proportion to each other as the numbers 3 , 5 , 7 , and 8. Ans . 12 , 20 , 28 , and 32 . 28. Divide the number 60 into 3 such parts , that of the first , of the second , and of the third , shall all be equal to each other . Ans . 12 ...
Page 131
... proportion of to 3 , which , being increased respectively , by 6 and 5 , are in the proportion of to ; required the numbers . Ans . 30 and 40 . 77. When the price of a bushel of barley wanted but 3 cents to be to the price of a bushel ...
... proportion of to 3 , which , being increased respectively , by 6 and 5 , are in the proportion of to ; required the numbers . Ans . 30 and 40 . 77. When the price of a bushel of barley wanted but 3 cents to be to the price of a bushel ...
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Common terms and phrases
added algebraic quantities apples arithmetical progression arithmetical series binomial bushels called cents a piece coefficient common difference complete equation Completing the square denotes Divide the number dividend division dollars entire quantity equal exactly divide exponent expression extract the square find the greatest Find the product Find the square Find the sum find the value following examples fourth fraction geometrical progression geometrical series Give an example greater greatest common divisor Hence last term least common multiple lemon letter minus monomial negative quantities number of terms peaches perfect square polynomial positive quantity pound of coffee preceding prime factors principle proportion pupil quan question quotient ratio Reduce remainder represent the cost represent the number required the numbers required to find result rule second degree solution square root subtracted theorem three numbers tion tities transposing unknown quantity whole number
Popular passages
Page 100 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 22 - Required the distance from A to B, from B to C, and from C to D.
Page 176 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 136 - In any proportion, the product of the means is equal to the product of the extremes.
Page 122 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Let x be the number of leaps taken by the hound.
Page 62 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 78 - To find the greatest common divisor of three or more quantities, first find the greatest common divisor of two of them ; then, of that divisor and one of the other quantities, and so on. The last divisor thus found, will be the greatest common divisor sought.
Page 59 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient.
Page 137 - A farmer has 2 horses, and a saddle worth 25 dollars ; now, if the saddle be put on the first horse, his value will be double that of the second ; but, if the saddle be put on the second horse, his value will be three times that of the first.
Page 219 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel in going 120 yards; but if the periphery of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel in the same space.